Cambridge Physics
5054 / 0625
Electric Current
by
Sir Junaid
syedpaf@gmail.com
4.2.2 Electrical current :
1. Define electric current as the charge passing a point per unit time; recall and use the equation
electric current = charge / time
I=Q/t
2. Describe electrical conduction in metals in terms of the movement of free electrons
3. Know that current is measured in amps (amperes) and that the amp is given by coulomb per second
(C / s)
4. Know the difference between direct current (d.c.) and alternating current (a.c.)
5. State that conventional current is from positive to negative and that the flow of free electrons is from
negative to positive
6. Describe the use of ammeters (analogue and digital) with different ranges
4.2.3 Electromotive force and potential difference
1. Define e.m.f. (electromotive force) as the electrical work done by a source in moving a unit charge
around a complete circuit;
recall and use the equation
e.m.f. = work done (by a source) / charge
E=W/Q
2. Define p.d. (potential difference) as the work done by a unit charge passing through a component; recall
and use the equation
p.d. = work done (on a component) / charge
V=W/Q
3. Know that e.m.f. and p.d. are measured in volts and that the volt is given by joule per coulomb ( J / C)
4. Describe the use of voltmeters (analogue and digital) with different ranges
5. Calculate the total e.m.f. where several sources are arranged in series
6. State that the e.m.f of identical sources connected in parallel is equal to the e.m.f. of one of the sources
4.2.4 Resistance
1. Recall and use the equation
resistance = p.d. / current
R=V/I
2. Describe an experiment to determine resistance using a voltmeter and an ammeter and do the
appropriate calculations.
3. Recall and use, for a wire, the direct proportionality between resistance and length, and the inverse
proportionality between resistance and cross-sectional area
4. State Ohm’s law, including reference to constant temperature
5. Sketch and explain the current–voltage graphs for a resistor of constant resistance, a filament lamp
and a diode
6. Describe the effect of temperature increase on the resistance of a resistor, such as the filament in a
filament lamp
4.3 Electric circuits
4.3.1 Circuit diagrams and circuit components
1. Draw and interpret circuit diagrams with cells, batteries, power supplies, generators,
oscilloscopes, potential dividers, switches, resistors (fixed and variable), heaters,
thermistors (NTC only), light-dependent resistors (LDRs), lamps, motors, ammeters,
voltmeters, magnetising coils, transformers, fuses, relays, diodes and light-emitting diodes
(LEDs), and know how these components behave in the circuit
4.3.2 Series and parallel circuits :
1. Recall and use in calculations, the fact that:
(a) the current at every point in a series circuit is the same
(b) the sum of the currents entering a junction in a parallel circuit is equal to the sum of the
currents that leave the junction
(c) the total p.d. across the components in a series circuit is equal to the sum of the
individual p.d.s across each component
(d) the p.d. across an arrangement of parallel resistances is the same as the p.d. across one
branch in the arrangement of the parallel resistances
2. Calculate the combined resistance of two or more resistors in series
3. Calculate the combined resistance of two resistors in parallel
4. Calculate current, voltage and resistance in parts of a circuit or in the whole circuit
4.3.3 Action and use of circuit components
1. Describe the action of negative temperature coefficient (NTC) thermistors and lightdependent resistors and explain their use as input sensors
2. Describe the action of a variable potential divider
3. Recall and use the equation for two resistors used as a potential divider
Main topics and sub-topics
removed:
•
Use of a manometer
•
Transmission of pressure in hydraulic
systems
Main topics and sub-topics added:
•
Motion (additional learning objectives)
•
Balanced and unbalanced forces
(additional learning objectives)
•
Equation for spring constant
•
Momentum
•
Principles of thermometry
•
Practical thermometers
•
The absolute scale of temperature
•
Latent heat (all learning objectives
removed except one)
•
General properties of waves
(additional learning objectives)
•
Methods of magnetisation and
demagnetisation
•
Simple magnetism and magnetic fields
(additional learning objectives)
•
Magnetic screening
•
•
•
Applications of electrostatic charging
Electronics and electronic systems
Equation for two resistors used as a
potential divider
•
Detection of radioactivity
(additional learning objectives)
•
Using decay equations
•
Space physics.
2
CURRENT ELECTRICITY
A flow of charges through a conductor in 1 second is called electric current.
The higher the current, the greater the flow of charge.
The SI unit of current is the ampere (A)
Conventional current direction is from positive to negative.
Electrons flow from negative to positive
CURRENT ELECTRICITY
The flow of charges through a conductor in 1 second is called electric current.
The SI unit of current is the ampere (A)
Conventional current direction is from positive to negative.
Electrons flow from negative to positive
Conventional current
Before the electron was discovered scientists agreed to think of current as
positive charges moving round a circuit in the direction from positive to negative
of a battery. This agreement still stands. Arrows on circuit diagrams show the
direction of what we call the conventional current, i.e. the direction in which
positive charges would flow. Electrons flow in the opposite direction to the
conventional current.
Current:
Current is the rate of flow of charges through a conductor.
�
I =
�
Q=I×t
Q= charges , I = Current , t = time
The electric current flowing in a circuit can be measured by
an AMMETER
How to use an Ammeter
Example question 1
In 10 second 60 C of charge flows around the circuit.
Calculate the current through the circuit.
Example question 2
A current of 150 mA flows around a circuit for 3 minute. How
much electric charge flows around the circuit in this time?
Example question 1
In 10 second 60 C of charge flows around the circuit. Calculate the
current through the circuit.
I =
�
�
=
��
=
��
6A
Example question 2
A current of 150 mA flows around a circuit for 3 minute. How
much electric charge flows around the circuit in this time?
First convert time into second = 3 × 60 = 180 sec
Then convert current into ampere = 150 / 1000= 0.15 A
Q=I×t
Q = 0.15 × 180 = 27 C
Direct current (d.c.)
A.C current
In a direct current (d.c.) the
electrons flow in one direction
only.
In an alternating current (a.c.)
the direction of electrons
flow reverses regularly.
Frequency of a.c.
The number of complete a cycles in 1 second is the frequency of the A.C.
The unit of frequency is the hertz (Hz).
The frequency of the a.c. in Figure is 2Hz,
which means there are two cycles per second, or one cycle lasts 1/2 = 0.5s.
The mains supply in many countries is a.c. of frequency 50Hz;
each cycle lasts 1 / 50 th of a second.
f=1/t
Key Points
Electric current is the rate of flow of electric charge and is
measured in amperes.
Conventional current assumes that charge carriers are positive,
meaning they flows away from positive terminals and towards
negative terminals.
Electron current is the actual flow of electrons, which flow in the
opposite direction of conventional current.
Electrons are not destroyed or used up in a circuit when there is
no current; they just stop moving.
Electromotive force (e.m.f):
e.m.f. is the work done by a source to move a unit charge around a
circuit.
Potential Difference or p.d:
p.d. is the work done by a unit charge to pass through a component in a
circuit.
e.m.f =
or V=
��������
�ℎ����
�
�
The S.I unit is Volt (V)
or E=
�
�
Potential difference (p.d) or Voltage
Energy carried by charges is consumed in components like
resistance, lamp, or heater of the circuit. When the charges flow
through the lamps in a circuit, their energy is converted other
forms such as heat and light.
The energy converted per unit charge passing through a
component is called potential difference (p.d), across the
component.
The p.d. across a component in a circuit is given by the work
done in the component/charge passed through the component.
p. � =
�
�
The unit of potential difference is volt (V)
Past Paper Question June 2020/ P22/Q10
An oscilloscope is a device used to display waveforms.
(a) Inside the oscilloscope, a beam of electrons is emitted
from a metal filament by thermionic emission. The emitted
electrons are accelerated away from the filament by a
potential difference of 2000V.
The charge on one electron is 1.6 × 10-19 C.
Calculate the maximum kinetic energy of one electron after it
has been accelerated through 2000V.
Past Paper Question June 2020/ P22/Q10
V = w / Q or V = E/ Q
2000 × 1.6 × 10-19
3.2 × 10-16 J
Cells in series
When cells are connected in series the combined
e.m.f. is the sum of all the individual e.m.f.’s.
Combined e.m.f. = 1.5V + 1.5V + 1.5V = 4.5V
Cells in parallels
When cells are connected in parallel, the combined
e.m.f. is the e.m.f. of one individual cell.
e.g.
Combined e.m.f. is 1.5 V
The advantages of connecting cells in parallel
The cell will last longer before they need to be
replaced.
A higher current can be supplied.
Now try this?
Calculate the combined e.m.f of the following cells.
The advantages of connecting cells in parallel
The cell will last longer before they need to be replaced.
A higher current can be supplied.
Now try this?
Calculate the combined e.m.f of the following cells.
Combined e.m.f = 2 + 2 + 2 = 6V
Potential difference across a component in a circuit is measured
by a voltmeter.
symbol
Resistance (R)
Resistance is the opposition to the flow of current.
The greater its resistance, the smaller the current that will flow through it.
SI unit of resistance is Ohm (Ω)
R=
Figure below shows a resistor
�
�
symbol
Worked example
Diagram shows a resistor connected in a circuit. The
current in the circuit shown in the ammeter is 2 A and
voltage across the resistor is 15 V. Calculate the
resistance of the resistor.
Worked example
Diagram shows a resistor connected in a circuit. The
current in the circuit shown in the ammeter is 2 A and
voltage across the resistor is 15 V. Calculate the
resistance of the resistor.
R=
R=
�
�
��
�
7.5 Ω
Measuring resistance
Connect a electrical component or a conducting wire
series to the battery and ammeter. Then connect the
voltmeter parallel to the electrical component or wire
as shown below.
Measure the voltmeter and ammeter reading in the
circuit. Resistance of the wire or electrical component
can be calculated by using the formula R= �
�
Factors affecting resistance
Resistance of a metal wire
(i) increases as its length increases
(ii) decreases as its cross-sectional area increases
(iii) depends on the material. (Silver, Gold , Copper)
(iv) increases as the temperature increases
Factors affecting resistance
Few factors to understand
The rate of flow of charges around a circuit is called the current.
Voltage is the force that pushes the current round the circuit.
If you increase the voltage, more current will flow.
If you increase the resistance, less current will flow.
Ways of decreasing the current in a circuit:
 Reducing the voltage from the battery.
 Increasing the resistance of the variable resistor.
The unit of...

Current - amp

Voltage - volt

Resistance - ohm
Factors affecting resistance
Length of wire
For a wire of uniform cross sectional area, the resistance is
proportional to the length of wire. The longer the wire, the further
electrons have to travel, the more likely they are to collide with
metal ions and so the greater the resistance. So if the length of
wire increases resistance also increases.
Cross-sectional area
For a wire fixed length, its resistance is inversely proportional to
the cross sectional area. The greater the cross sectional area of the
wire, the more electrons there are available to carry charge along
the wire length and so the lower resistance. So if cross-sectional
area of a wire increases resistance of the wire decreases.
Temperature
For metallic wires, as temperature increases, the
resistance of it also increases. But for some materials like
silicon and germanium (semiconductors), as temperature
increases resistance decreases.
Material
Resistance depends on the kind of substance.
Copper is a good conductor and is used for connecting
wires. But Nichrome has more resistance and is used in
the heating elements of electric heater.
Few factors to understand
 Current flows from positive to negative.
 An ammeter should be connected in series with a component.
 Items that are in series can be in any order.
 A voltmeter should be connected in parallel with a component.
Rheostat
A variable resistor or rheostat is used to vary the current in a
circuit. A sliding contact moves, it varies the length of the wire in
the circuit and hence the resistance will be changed.
Effect of temperature on resistance
The circuit below can be used to investigate how current trough
a conductor depends on the p.d. across it. The conductor in this
case is a coiled-up length of nichrome wire, kept at a constant
temperature by immersing it in a large amount of water. The p.d.
across nichrome wire can be varied by adjusting variable resistor.
Typical results are shown in the table and graph below.
Current / A p.d. / V
Resistance / Ω
0.2A
1V
5Ω
0.4A
2V
5Ω
0.6A
3V
5Ω
0.8A
4V
5Ω
1A
5V
5Ω
Ohm’s Law:
The current in a conductor is directly proportional to the
potential difference (Voltage )applied to the conductor.
V∝I
or
V = IR
Series Circuits
 Components that are connected
one after another on the same
loop of the circuit are connected
in series.
 The current that flows across
each component connected in
series is the same.
Parallel Circuits
 Components that are
connected on separate
loops are connected in
parallel.
 The current is shared
between each
component connected in
parallel.
Ohm’s Law:
The current in a conductor is directly proportional to the p.d
applied to the two ends of the conductor.
The current flowing through a conductor is directly proportional
to the voltage.
Ohm’s Law:
The current in a conductor is directly proportional to the p.d
applied to the two ends of the conductor.
The result in the table shows that when the voltage
increases the current also increases within constant
temperature. And the gradient of the graph is constant
value (voltage / current is equals to constant value of
resistance).
So we can conclude that under constant temperature
voltage is directly proportional to the current. This is
called Ohm’s law.
We can use the data to plot a graph of current against
potential difference for a resistor. This graph is shown in Figure and is
known as a current–voltage characteristic.
• The p.d. V is on the x-axis, because this is the quantity we vary. It is the
independent variable.
• The current I is on the y-axis, because this is the quantity that varies as we
change V. It is the dependent variable.
In this case, the graph is a straight line that passes through the origin. This is
what we expect because the quation I = shows that the current I is
proportional to the p.d., V
The resistance of the most of the conductors becomes
higher if the temperature of the conductor increases. As
the temperature rises, the metals ions vibrate more and
provide greater resistance to flow the electrons. For
example filament lamp, as the current flows through
the metal filament, it gets hotter so its resistance
increases. This means the current varies with voltage is
not directly proportional and not give straight line for
current-voltage graph.
Series Circuits
Q1. Add following resistors
(a) in series
(b) in parallel
(i) 4 ohm and 6 ohm
(ii) 4 ohm and 4 ohm
(iii) 2 ohm and 6 ohm
(iv) 3 ohm and 6 ohm
(c) Both
Resistors in series
The total resistance R of the resistors connected in series circuit
is equals to the sum of the separate resistance.
Resistors in parallel
The effective resistance R of the resistors connected in parallel can be calculate
by using the formula:
Resistors in series
The total resistance R of the resistors connected in series circuit
is equals to the sum of the separate resistance.
R = R1 + R2
R = R1 + R2 = 2 + 8 = 10Ω
Resistors in parallel
The effective resistance R of the resistors connected in parallel can be
calculate by using the formula:
R =
R =
�� × ��
�� + ��
� �
�+ �
= 1.43Ω
Now try this?
Calculate the effective resistance of the following resistors?
Now try this?
Calculate the effective resistance of the following resistors?
R = R1 + R2
R = 2 + 8 = 10
R =
�� × ��
�� + ��
R = R1 + R2
R = 5 + 5 = 10
R =
�� ��
�� +��
=5Ω
D.C. Circuits
Series circuit:
Q1. Find the p.d across each resistor.
Q2. Find the current in each resistor.
When resistors or other components are connected in series:
§ the current at every point in a circuit is the same.
D.C. Circuits
When resistors or other components are connected in series:
§ the current at every point in a circuit is the same.
Total resistance = R1 + R2 = 10Ω
V = IR
I = V / R = 16 / 10 = 1.6A
So the ammeter reading shown in
the circuit is 1.6A and the current
in each resistor is also 1.6A.
D.C. Circuits
Series circuit:
Q1. Find the unknown resistor, when current is 1.6 A.
When resistors or other components are connected in series:
§ the current at every point in a circuit is the same.
Question from Hodder page 213
A p.d. of 24 V from a battery is applied to the network of
resistors in Figure.
(a) What is the combined resistance of the 6 Ω and 12 Ω resistors.
(b) What is the current in the 8 Ω resistor?
(c) What is the power of 8 ohm resister?
(d) What is the voltage accross 8 ohm?
Question from Hodder page 213
A p.d. of 24 V from a battery is applied to the network of
resistors in Figure.
(a) What is the combined resistance of the 6 Ω and 12 Ω resistors.
(b) What is the current in the 8 Ω resistor?
Past paper Question (Nov. 2014/P1/Q26)
Past paper Question (Nov. 2012/P1/Q29)
§ the sum of the potential differences in a series circuit is equal to the
potential difference across the whole circuit
P.d across 6Ω resistor
V = IR = 1.6 x 6 = 9.6V
P.d across 4Ω resistor
V = IR = 1.6 x 4 = 6.4V
P.d across the circuit = 9.6 + 6.4 = 16 V
Parallel circuits
When resistors or other components are connected in parallel:
§ the P.d at every point in a circuit is the same.
P.d across each resistor is 18V
§ the current from the source is the sum of the currents in
the separate branches of a parallel circuit.
Current across 8Ω resistor
V = IR
I = V / R = 18 / 8 = 2.25A
Current across 2Ω resistor
V = IR
I = V / R = 18 / 2 = 9A
So sum of the currents in the separate branches is (2.25 +9 = 11.25A ) and is equals to
current from the source as shown in the ammeter reading in the diagram above.
Advantages of connecting electrical components in
parallel
There are some advantages of connecting lamps and other
electrical components in parallel rather than connecting in
series. These include:
 The voltage through each lamp is same so each lamp has same
brightness.
 If the one lamp is melt the other lamps will work but in series
if one lamp melts others will not work.
 In series total resistance of bulb will be increased.
Electrical symbols
Lamps
Ammeter
Voltmeter
AC power supply
Switch
Cell (battery) several cells
DC power supply
Resistor
Variable resistor
Light dependent resistor
Fuse
Diode
Light emitting diode
Magnetising coil
Electric bell
Relay
Draw a circuit diagram including:
(i) a 15 V power supply of fixed voltage,
(ii) Two resistors connect in parallel each rating 5Ω
(iii)A switch
(iv) an ammeter to measure the current trough the circuit
(v) Variable resistor
Draw a circuit diagram including:
(i) a 1.5 V power supply of fixed voltage,
(ii) Two bulbs connected in series
(iii) A switch
(iv) an ammeter to measure the current through the circuit
(v) Volt meters across each bulb to measure the p.d across the bulbs.
LDR:
Light dependent resistor –
resistance decreases when light
intensity increases.
Thermistor:
Thermistor – resistance decreases
when temperature increases.
Diode:
Diode – only lets current flow in
one direction
LDR:
gf
Rheostat:
An electrical instrument used to control a current by varying the
resistance.
Light dependent resistor (LDR)
A light dependent resistor (LDR) is a type of variable resistor
whose resistance depends on the amount of light falling on it .
An LDR is made of material that does not normally conduct
well (semiconductor Cadmium Sulphide). In the dark, an LDR
has a high resistance, often over 1MΩ. However, light can
provide the energy needed to allow a current to flow. Shine
light on an LDR and its resistance decreases. In bright light its
resistance may fall to 400Ω).
LDRs are used in circuits to detect the level of light, for
example in security lights that switch on automatically at night.
symbol
Q11. Fig. 11.2 is a circuit used to monitor changes in room temperature.
A thermistor is connected in series with a 6.0 V battery and a 2000Ω
resistor.
(i) The temperature of the room increases. State and explain what happens
to
1. the reading on the ammeter,
[2]
2. the reading on the voltmeter.
[2]
(ii) At a certain temperature, the reading on the voltmeter is 3.8 V.
Calculate the resistance of the thermistor at this temperature.
[3]
June 2010/ P2/ Q11